Answer
$\dfrac{5\sqrt{2}}{2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{\dfrac{25}{2}}
,$ evaluates to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{25}{2}\cdot\dfrac{2}{2}}
\\\\=
\sqrt{\dfrac{25}{4}\cdot2}
\\\\=
\sqrt{\left( \dfrac{5}{2} \right)^2\cdot2}
\\\\=
\dfrac{5}{2}\sqrt{2}
\\\\=
\dfrac{5\sqrt{2}}{2}
.\end{array}
